Question

Suppose sin(A)=-0.78. use the trig identity sin^2(A)+cos^2(A)=1 and the trig identity tan(A) = sin(A)/cos(A) to find tan(A) in quadrant IV. round to the ten-thousandth.

a. -0.2039
b. 1.3941
c. 0.8671
d. -1.2464

Answer 1

In quadrant IV,
`\cos(A)` is positive. So

`\sin^2(A) + \cos^2(A) = 1 \implies \cos(A) = √(1-\sin^2(A)) \approx 0.6258`

Then by the definition of tangent,

`\tan(A) = (\sin(A))/(\cos(A)) \approx (-0.78)/(0.6258) \approx \boxed{-1.2465}`